PORTB0 (Arduino D8) can be set to output the system clock. I once read, but can no longer find, a post by someone who wrote code to read the clock frequency and correct their timer for it.

I'm looking to create a clock. It doesn't have to be super-amazingly accurate, but the ~1sec/5min loss I'm getting with a 32.768 kHz crystal is not acceptable. I'm thinking the crystal's slow because it's at room temp, not skin temp--so I'm considering a TCXO (DigiKey no. DS32KHZ/DIP-ND), but I've read that the ATmega may not be designed for that. Could I just send the signal from that to TOSC1 for TIMER2 running asynchronously?

Still not clear exactly what you're trying to do, and exactly what the problem is. What is being used for the system clock, and what is the 32kHz crystal connected to? If you're clocking timer 2 from the 32kHz crystal, then that is not the system clock, so it cancan't be output to the CLKO pin. One second in 5 min is 3333ppm, so something is terribly wrong. What is the load capacitance spec for the crystal? I've got a lot of DS1307s with 32kHz crystals around, most run within 20ppm, although I do have one or two flyers. I'd go for a Chronodot (±2ppm) or something similar before I'd go for that $12 TXCO (±7.5ppm).

A lot of the 32.768kHz crystals that get used with DS1307s have a load capacitance spec of 12.5pF. These will also work to clock timer2 asynchronously; I've done this once or twice just playing around, but haven't measured the frequency.

One second in 5 min is 3333ppm, so something is terribly wrong. What is the load capacitance spec for the crystal? I've got a lot of DS1307s with 32kHz crystals around, most run within 20ppm, although I do have one or two flyers. I'd go for a Chronodot (±2ppm) or something similar before I'd go for that $12 TXCO (±7.5ppm).

I've got the µC running at 8MHz internal osc; the watch crystal is hooked up to TOSC1/2 not on the breadboard--I bent the legs up and taped it on to avoid parasitic capacitance. Atmel note AVR4001 has a graph which shows frequency increasing with less capacitance and decreasing with more. I have crystals with 6pF, 8pF, and 12.5pF load capacitance. Right now I'm using the 12.5.

It does rather seem like something is very wrong--the datasheet for the DS32KHZ has a graph showing its ppm delta time compared to a non-compensated crystal, and at 15ºC (room temp here) the regular crystal should be max -40 ppm. I don't know.

From that datasheet, it seems that TCXO does have ±2 ppm stability in non-extreme temp ranges. But the ChronoDot (which is more expensive) comes with a battery and battery holder, which is nice... and it seems it can output a 32.768 kHz signal, which I'd want, as my binary clock uses up a lot of pins. Maybe I will do that.

If this is a clock project, why not use an external RTC. Yes most can supply a 32.768kHz signal, but that's just using it as a TXCO, when it has all the time, date, alarm, etc. functionality built in as well. Another option is to just use the chip (DS3231) as in the Chronodot or one of its siblings (DS3232, DS3234). They're not cheap, $9 or $10, so by the time the backup battery and all is added, it'd probably cost as much or more as the Chronodot.

Here's my blog post on the experiment I did, I just stuck the crystal in the breadboard. I don't remember checking accuracy, but if it was way off, I would have probably noticed. But it was strictly an experiment; it worked and I didn't worry about finer points like accuracy. But yes those breadboards do add some capacitance to things. But the tape business sounds pretty sketchy as well